I. RECONFIGURABLE ROBOTS a.) Solved the hinged dissection problem, which was over a 100 years old, proving that any finite collection of shapes have a hinged dissection. b.) Proved that crystalline robots can reconfigure extremely efficiently: O(log n) time and O(n) moves. c.) Proved that any orthogonal polyhedron can be folded from a single, universal crease pattern (box pleating). II. ORIGAMI DESIGN a.) Developed mathematical theory for what happens in paper between creases, in particular for the case of circular creases. b.) Circular crease origami on permanent exhibition at MoMA in New York. c.) Developing mathematical theory of Tomohiro Tachi's Origamizer framework for efficiently folding any polyhedron from a sheet of paper. d.) Developing mathematical theory of Robert Lang's TreeMaker framework for efficiently folding tree-shaped origami bases.